The power is out Sunday afternoon along High Ridge Road in the Bulls Head area of Stamford.
Connecticut Light & Power reports 1,244 customers are without power in the 93-degree heat. The outage occurred about 2:30 p.m.
At least one high-profile CL&P customer, Lord & Taylor, is among those affected.
Cooling centers in the city are open until 6 p.m. Sunday. For more information, visit stamfordct.gov.
UPDATE (7:03 p.m.): Power has been restored to all but 5 customers.